Preheat oven to 400 degrees F. Grease 12 standard muffin-pan cups. In large bowl, combine oats, flour, sugar, baking powder, baking soda, salt, and ground cinnamon.
In medium bowl, with fork, beat buttermilk, oil, and egg until well blended; stir in shredded apples. Add apple mixture to flour mixture, and stir just until flour mixture is moistened (batter will be very thick and lumpy). Stir in chopped walnuts.
Spoon batter into prepared muffin-pan cups. Bake 23 to 25 minutes or until muffins begin to brown and toothpick inserted in center of muffins comes out clean. Immediately remove muffins from pan. Serve warm, or cool on wire rack to serve later.